VARIATIONAL BOUND ON ENERGY-DISSIPATION IN PLANE COUETTE-FLOW

We present numerical solutions to the extended Doering-Constantin vari ational principle for upper bounds on the energy dissipation rate in t urbulent plane Couette flow. Using the compound matrix technique in or der to reformulate this principle's spectral constraint, we derive a s ystem of equations that is amenable to numerical treatment in the enti re range from low to asymptotically high Reynolds numbers. Our variati onal bound exhibits a minimum at intermediate Reynolds numbers and rep roduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wave numbers, there exist two length s cales that determine the optimal upper bound: the effective width of t he variational profiles' boundary segments and the extension of their flat interior part.